2013·广东韶关·一模
1 . 如图,长方体
中,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/17b118f7d08842de8760eab70ffafea3.png)
(1)求三棱锥
的体积;
(2)证明:
;
(3)求二面角
的正切值.
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/c22f0b58ffe5470ea706d123e0272507.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/626c7aca1d3346abbf7a9496eb082201.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/8fbf6d33e2c04ac4a2d45c3ad41921cf.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/01f8ce7444db463e81894180db143bbf.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/17b118f7d08842de8760eab70ffafea3.png)
(1)求三棱锥
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/36a589513be945a9ba8516dcb231e552.png)
(2)证明:
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/e87cf8bd2b834ffea09730874247c0e1.png)
(3)求二面角
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/7f7c097034cf470ab64b2a690a78fb40.png)
您最近一年使用:0次
2 . 如图,在三棱锥
中,平面
平面
,
,
,过
作
,垂足为
,点
分别是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/5e6ed79619724f8a995e4e288d71fa05.png)
求证:(1)平面
平面
; (2)
.
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/b8b4627e0ee746b6a869b7c0518e7c50.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/4dde54b789a045e299bd3d347b0f33fe.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/a0abd3dff20f4df78d34d33ccc3958be.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/668354606a1b42a7a43170ced66bdb70.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/c57030df5014430e8803442c1585e31e.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/7733030cd3bd415c9ea3908b2140e5ac.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/12222ea1107d4aaca273fc766d954b7d.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/dd4c6c9bac7d4143a2f65e19893451c5.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/2288524aa5c04a7192c6e88318aef7dc.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/fababe80039d4339ba0094fc6b0e886d.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/5e6ed79619724f8a995e4e288d71fa05.png)
求证:(1)平面
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/8a9bad60b51d4a6393ed4a923b102964.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/4ec3160b173a486f849f9707554229a5.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572177749975040/1572177755856896/STEM/db54de8cdaf74f62a6c9b6da522746b5.png)
您最近一年使用:0次
3 . 如图,
是半径为
的半圆,
为直径,点
为
的中点,点
和点
为线段
的三等分点,平面
外一点
满足
平面
,
.
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/04632768d1524054a33db6076799e2ca.png)
(1)证明:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/3fb4308cc4024daea54217935a902f43.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/5ca566db478945e397a19f3ff6a67e8b.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/fe80ee3aa02c4773bb790f6980a9cef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/030b4dcd10654a07b400fab2bcdfb45a.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/a8cfdf7ab62b4a02bbc36353f7be767c.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/3546f7c57fc64148b5e6f45eadeba0b4.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/6868bd0380a44a74aa371b219af30ef0.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/94a7b841abac4a5b9068f80ec5153899.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/d0d033e0948343ce926a7f075e514bdd.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/e5939a524876480f8d81b59a7d218146.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/ed509aa771b94ef1b9dfcd696159673d.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/04632768d1524054a33db6076799e2ca.png)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/70db6c961a75483d938cede2927c8e52.png)
(2)求点
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/030b4dcd10654a07b400fab2bcdfb45a.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497880064/STEM/16b8c3810d5b40f69a346421914b90c0.png)
您最近一年使用:0次